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To find the mean and variance of a random variable

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I don't understand probabilities much. Could you please explain the attached question? Thank you.

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Solution Summary

This solution gives the condition for a function to be a density function and to find its mean and variance.

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Finding the Mean and Variance of Random Variables

Dealers profit is a random variable, x, having the probability density shown below.

f(x) = 2(1 - x) 0 < x < 1
0 elsewhere

a) Find the mean of x

b) Find the variance of x

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